Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces


Autoria(s): Robinson, James C.; Sadowski, Witold; Silva, Ricardo P.
Contribuinte(s)

Universidade Estadual Paulista (UNESP)

Data(s)

30/09/2013

20/05/2014

30/09/2013

20/05/2014

01/11/2012

Resumo

Suppose that u(t) is a solution of the three-dimensional Navier-Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we show that the norm of u(T - t) in the homogeneous Sobolev space (H)over dot(s) must be bounded below by c(s)t(-(2s-1)/4) for 1/2 < s < 5/2 (s not equal 3/2), where c(s) is an absolute constant depending only on s; and by c(s)parallel to u(0)parallel to((5-2s)/5)(L2)t(-2s/5) for s > 5/2. (The result for 1/2 < s < 3/2 follows from well-known lower bounds on blowup in Lp spaces.) We show in particular that the local existence time in (H)over dot(s)(R-3) depends only on the (H)over dot(s)-norm for 1/2 < s < 5/2, s not equal 3/2. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4762841]

Formato

15

Identificador

http://dx.doi.org/10.1063/1.4762841

Journal of Mathematical Physics. Melville: Amer Inst Physics, v. 53, n. 11, p. 15, 2012.

0022-2488

http://hdl.handle.net/11449/25142

10.1063/1.4762841

WOS:000311964100019

WOS000311964100019.pdf

Idioma(s)

eng

Publicador

American Institute of Physics (AIP)

Relação

Journal of Mathematical Physics

Direitos

closedAccess

Palavras-Chave #Navier-Stokes equations
Tipo

info:eu-repo/semantics/article